Intangible Assets, Net - Summary of Intangible Assets (Details) - USD ($) $ in Millions	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Not subject to amortization
Total intangible assets not subject to amortization	$ 438.6	$ 459.9
Subject to amortization
Intangibles subject to amortization Cost	937.0	943.2
Total intangible assets	1,375.6	1,403.1
Intangible assets - Accumulated Amortization	480.9	433.3
Total	456.1	509.9
Total intangible assets - Net	894.7	969.8	$ 987.6
Customer relationships
Subject to amortization
Intangibles subject to amortization Cost	818.2	831.4
Intangible assets - Accumulated Amortization	401.8	368.7
Total	416.4	462.7
Patents
Subject to amortization
Intangibles subject to amortization Cost	19.2	19.2
Intangible assets - Accumulated Amortization	11.0	8.7
Total	8.2	10.5
Software
Subject to amortization
Intangibles subject to amortization Cost	80.3	72.2
Intangible assets - Accumulated Amortization	58.9	48.5
Total	21.4	23.7
Other
Subject to amortization
Intangibles subject to amortization Cost	19.3	20.4
Intangible assets - Accumulated Amortization	9.2	7.4
Total	10.1	13.0
Trademarks
Not subject to amortization
Total intangible assets not subject to amortization	437.2	459.2
Intellectual Property
Not subject to amortization
Total intangible assets not subject to amortization	$ 1.4	$ 0.7